A191554 a(n) = Product_{k=1..n} prime(k)^(2^(k-1)).

2, 18, 11250, 64854011250, 2980024297506569894680811250, 1319492964487055911863581348741902326769016593763234907139211250

Offset

1,1

Comments

x^(2^n) - a(n) is the minimal polynomial over Q for the algebraic number sqrt(p(n)*sqrt(p(n-1)*...*sqrt(p(2)*sqrt(p(1)))...)), where p(k) is the k-th prime. Each such monic polynomial is irreducible by Eisenstein's Criterion (using p = 2).

Links

Table of n, a(n) for n=1..6.

Formula

For n > 1, a(n) = a(n-1) * prime(n)^(2^(n-1)); a(1) = prime(1).

Example

a(1) = 2^1 = 2 and x^2 - 2 is the minimal polynomial for the algebraic number sqrt(2).
a(4) = 2^1*3^2*5^4*7^8 = 64854011250 and x^16 - 64854011250 is the minimal polynomial for the algebraic number sqrt(7*sqrt(5*sqrt(3*sqrt(2)))).

Prog

(PARI) a(n) = prod(k=1, n, prime(k)^(2^(k-1)))

Crossrefs

Cf. A191555.

Sequence in context: A309972 A208056 A276092 * A066361 A120929 A349886

Adjacent sequences: A191551 A191552 A191553 * A191555 A191556 A191557

Keyword

nonn,easy

Author

Rick L. Shepherd, Jun 05 2011

Status

approved